Search for a tool
Permutations

Tool to generate permutations of items, the arrangement of distinct items in all possible orders: 123,132,213,231,312,321.

Results

Permutations -

Tag(s) : Combinatorics

Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Feedback and suggestions are welcome so that dCode offers the best 'Permutations' tool for free! Thank you!

# Permutations

## Permutations Generator

 Separator Comma ',' None

### Partial Permutations Generator

⮞ Go to: K-Permutations

### Combinations Generator

Permutations are often confused with combinations (n choose k). dCode has a tool for that:

## Permutations/Anagrams Calculator

### Random Permutation

⮞ Go to: Random Selection

### What is a permutation? (Definition)

In Mathematics, item permutations consist in the list of all possible arrangements (and ordering) of these elements in any order.

Example: The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).

### How to generate permutations?

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Here is a pseudo code source : function permute(data, n) { if (n = 1) print data else { for (i = 0 .. n-2) { permute(data, n-1) if (n % 2) swap(data[0], data[n-1]) else swap(data[i], data[n-1]) permute(data, n-1) } }}

Permutations can thus be represented as a tree of permutations:

### How to count permutations?

Counting permutations uses combinatorics and factorials

Example: For $n$ items, the number of permutations is equal to $n!$ (factorial of $n$)

### How to count distinguishable permutations?

Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.

Example: DCODE 5 letters have $5! = 120$ permutations but contain the letter D twice (these $2$ letters D have $2!$ permutations), so divide the total number of permutations $5!$ by $2!$: $5!/2!=60$ distinct permutations.

## Source code

dCode retains ownership of the "Permutations" source code. Except explicit open source licence (indicated Creative Commons / free), the "Permutations" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Permutations" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Permutations" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

## Cite dCode

The copy-paste of the page "Permutations" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Permutations on dCode.fr [online website], retrieved on 2023-05-31, https://www.dcode.fr/permutations-generator

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!